Handbook of the History of Logic: - Fordham University Faculty

The Latin Tradition of Logic to 1100 39
1611), containing the whole set of monographs, seems (from a note it contains)
to have this material from a collection of Boethius’s works put together in Constantinople
in the 520s [Van de Vyver, 1935, 131-2]. Whether (as most scholars
believe) the exemplar was brought to Europe from Byzantium in the tenth century,
or it was simply studied and copied for the first time in this period, this rediscovery
would have an important effect on how logic was studied. With regard to
syllogistic, both surviving manuscripts and library catalogues show that, after the
tenth century, there was a turn from using Apuelian theory (directly from his Peri
Hermeneias, or indirectly from the encyclopaedias) to using Boethius’s treatises
[Sullivan, 1967, 193-203]. The theory of the Topics, now much more conveniently
available in the On Topical differentiae than before through the commentary on
Cicero and the encyclopaedic accounts, would become one of logicians’ main concerns
by the twelfth century.
The three outstanding logicians of the period are also those in whom the new
developments can be seen with especial clarity: tentatively in Notker of St Gall,
more definitely in Gerbert of Aurillac and most obviously in Abbo of Fleury.
4.1 Notker of St Gall
St Gall had been an important centre for logic since the ninth century (see above,
p. 36). Notker Labeo (c. 950–1022) continued this tradition, especially within his
project of translating central school-texts into the vernacular, Old High German.
Of the four works he chose to translate, two were logical — a mark of the prominence
of the subject in the curriculum, especially since the other two translations
(Books I and II of Martianus Capella; Boethius’s Consolation) were general philosophical
works rather than texts of a particular discipline. Moreover, the two texts
were both Aristotle: the Categories and On Interpretation, and to the German
version some Latin glosses, mainly based on Boethius’s commentaries, are added
[Notker the German, 1972; 1975]. Notker is therefore, in this way, a pioneer of the
new Boethian logic.
Yet the most sophisticated of the writings attributed to him, On Syllogisms
[Piper, 1882, 597-622], is based closely on works known since the ninth century:
Apuleius’s Periermenias for categorical syllogisms, and, for the hypothetical syllogisms,
Boethius’s commentary on Cicero’s Topics and Martianus Capella. By
basing himself ultimately on Cicero, Notker produces an account a little nearer
the Stoics than he could have found in On Hypothetical Syllogisms, had he known
it — and he even copies [Notker, 1882, 610-11] from Martianus Capella (cf. p. 6)
a presentation of the modes using numbers. But his conception of hypothetical
syllogisms is thoroughly Boethian, as his adopting Boethius’s deviant form of the
third mode indicates. He even elaborates this third mode, because he thinks its
major premiss can be formed by preposing a negation to a contradiction of all four
forms:- (1) ‘If it is day, it is night’; (2) ‘If it is not day, it is not night’; (3) ‘If it is
day, it is not light’; (4) ‘If it is not day, it is light.’ He has given some thought to
how this mode ‘arises from the first two’: